Method and System for Tracking Eigenvalues of Matrix Pencils for Signal Enumeration

1. In a method for signal enumeration for performing blind source separation of plural signals in a multi-signal environment, the improvement comprising the step of tracking eigenvalues of matrix pencils over successive frames where at least one of the matrix pencils is a function of one of said plural signals to thereby enumerate the signals.

2. In a method for signal enumeration for performing blind source separation of plural signals in a multi-signal environment, the improvement comprising the step of tracking eigenvalues of matrix pencils where at least one of the matrix pencils is a function of one of said plural signals: collecting frames of data from the plural signals; providing an estimate of at least one matrix pencil from one of the frames; deriving an eigenvalue from one of the matrix pencil estimates; associating the eigenvalue by either assigning the eigenvalue to an existing track of eigenvalues plotted on a complex plane or assigning the eigenvalue to a new track on the complex plane as a function of a set of predetermined criteria; performing eigenvalue track maintenance operations; and, updating signal enumeration estimates.

3. The method of claim 2 wherein the step of providing an estimate of at least one matrix pencil comprises the step of determining a higher order statistic.

4. The method of claim 3 wherein the higher order statistic is a 2 nd order moment.

5. The method of claim 3 wherein the higher order statistic is a spatial 4 th order cumulant.

6. The method of claim 2 wherein the step of performing track maintenance operations comprises at least one of the steps selected from the group consisting of initiating a new track, deleting a track, upgrading a track, or continuing a track.

7. The method of claim 6 wherein the step of performing track maintenance operations is performed on each track based on eigenvalue assignments.

8. The method of claim 6 wherein the step of initiating a new track comprises the step of creating a new track associated with an unmatched eigenvalue.

9. The method of claim 6 wherein the step of deleting a track is performed when said track is not assigned an eigenvalue for a predetermined number of frames of data.

10. The method of claim 9 wherein the predetermined number is greater than one.

11. The method of claim 6 wherein the step of upgrading a track is performed when a track is assigned an eigenvalue from the frame of data.

12. The method of claim 6 wherein the step of continuing a track is performed when a confirmed track is not assigned an eigenvalue from the frame of data.

13. The method of claim 2 wherein the step of deriving an eigenvalue comprises the step of performing eigenvalue decomposition of a matrix pencil.

14. The method of claim 2 wherein the frame comprises a plurality of signal snapshots from a plurality of sensor elements.

15. The method of claim 14 wherein the plurality of signal snapshots is less than 5000.

16. The method of claim 2 wherein ones of successive frames are overlapping.

17. The method of claim 2 further comprising the step of checking track association validity.

18. In a method of blind source separation of plural signals in a multi-signal environment in which the number of signals is unknown, the improvement comprising the step of determining the number of unknown signals as a function of block-wise tracking over successive blocks of eigenvalues derived from the plural signals.

19. The method of claim 18 wherein the multi-signal environment includes noise.

20. The method of claim 19 wherein the step of tracking eigenvalues is accomplished independent of the type of waveform of the plural signals.

21. The method of claim 19 wherein the step of tracking eigenvalues is accomplished independent of the character of the noise.

22. A method of estimating M number of signals received as a composite signal by an N element array independent of any parameters of the M signals, where M≦N comprising the steps of: (a) collecting plural frames of data at predetermined time intervals from the N element array; (b) deriving a plurality of eigenvalues from a frame of data; (c) associating each eigenvalue by either assigning the eigenvalue to an existing track of eigenvalues plotted on a complex plane or assigning the eigenvalue to a new track on the complex plane as a function of a set of predetermined criteria; (d) adjusting a state of the eigenvalue tracks; and, (e) determining an estimate for M as a function of the number of eigenvalue tracks mat least one predetermined state.

23. The method of claim 22 comprising the step of repeating steps (b) through (e) for successive frames of data.

24. The method of claim 22 wherein the state of an eigenvalue track is selected from the group consisting of new, tentative, candidate, and confirmed.

25. The method of claim 22 further comprising the step of deleting an existing track of eigenvalues when said track is not assigned an eigenvalue for a predetermined number of frames of data.

26. The method of claim 25 wherein the predetermined number of frames of data is greater than one.

27. The method of claim 22 wherein the step of assigning an eigenvalue to an existing track is a function of the Euclidean distance between said eigenvalue and said existing track.

28. In a method for signal enumeration for blind source separation of plural signals in a multi-signal environment including noise, the improvement comprising the step of mapping eigenvalues of matrix pencils in a complex plane over successive frames where at least one of the matrix pencils is a function of one of the plural signals to thereby enumerate the plural signals.

29. In a method for determining the number of signals in a multi-signal environment with noise, the improvement of distinguishing a first one of the plural signals from the others of the plural signals and from the noise as a function of the frame to frame stability of a series of eigenvalues in a complex plane that are derived from a characteristic of the first signal over a predetermined number of time intervals.

30. A system for signal enumeration in a multi-signal environment, comprising: means for collecting frames of data from the plural signals; means for providing an estimate of at least one matrix pencil from one of the frames; means for deriving an eigenvalue from one of the matrix pencil estimates; means for associating the eigenvalue by either assigning the eigenvalue to an existing track of eigenvalues plotted on a complex plane or assigning the eigenvalue to a new track on the complex plane as a function of a set of predetermined criteria; means for performing eigenvalue track maintenance operations; and, means for updating signal enumeration estimates.

31. In a system for signal detection and enumeration having a multi-element array, a receiver and an eigenvalue generator, the improvement comprising: an eigenvalue location processor for block-wise mapping of eigenvalues on a complex plane; and, a counter for recording a predetermined number of eigenvalues that are mapped in substantially the same location on the complex plane in successive blocks.

32. A method of signal detection comprising the steps of determining a matrix pencil from a high order statistic of digitized sensor data, performing generalized eigenvalue decomposition, and tracking a location of an eigenvalue in a complex plane in successive frames of digital data to thereby detect the signal.

33. A system for detecting a communication signal having a plurality of symbols each formed from a sequence of bits, comprising: a receiver for receiving and digitizing successive frames of the symbols of said communication signal; means for determining a matrix pencil eigenvalue for at least one of said symbols for each of a plurality of said frames; means for determining the generalized eigenvalue decomposition of said matrix pencil eigenvalues; means for mapping said eigenvalues on a complex plane; and, means for determining the relationship between one eigenvalue in a first frame and a corresponding eigenvalue in a subsequent frame to thereby detect the signal.

34. The system of claim 33 wherein the communication signal is in a multi-signal environment.

35. The system of claim 33 wherein the communication signal is in a noisy environment.

36. The system of claim 33 wherein the means for determining the relationship between eigenvalues comprises determining the Euclidean distance in the complex plane between the eigenvalues.